Symmetry Maps and Transforms for Perceptual Organization and Object Recognition
Thursday, November 16, 2000 - 2:00pm - 3:00pm
Benjamin Kimia (Brown University)
Traditionally, symmetry set representations have been defined for segmented shape. However, the difficulties in obtaining shape from gray-level images have led us to consider the direct acquisition of symmetry maps from gray-level images. In this talk, we propose that the symmetry map of an edge map is an appropriate intermediate level representation between low-level edge maps and high-level object models, and that transformations of it are canonical building blocks for perceptual grouping and object recognition. First, we review our approach for computing the symmetries (skeletons) of an edge map (and shape) consisting of a collection of curve segments. This approach is a combination of analytic computations in the style of computational geometry and discrete propagations on a grid in the style of the numerical solutions of PDE's as in curve evolution. This framework results in (i) analytically exact solutions, (ii) near optimal computational complexity, (iii) local computations, and (iv) a graph representation which can be used in applications such as object recognition. Second, we present symmetry transformations on the symmetry map as a language for perceptual organization. Specifically, it is proposed that (i) a symmetry map can fully represent the initial edge map so that both boundary and regional continuities can be represented via skeletal/shock continuity; (ii) a re-organization of the edge map in the form of completing gaps, discarding spurious elements, smoothing, and partitioning a contour (grouped set of edge elements) can be represented by transformations on the symmetry map; (iii) perceptual grouping and object recognition can be cast as finding the least action path in the space of sequences of symmetry transforms.